Probability Concepts in Finance Review

A martingale is a stochastic process with the property that, at any particular time in the realized sequence, the expectation of the next value in the sequence is equal to the present observed value.

Itô's formula is a fundamental result in stochastic calculus that provides a formula for the total differential of a function of a stochastic process. It is essential for deriving differential equations involving stochastic processes.

Girsanov's theorem is a key result in stochastic calculus that allows for changing the measure under which a stochastic process is modeled. It is important in finance for pricing financial derivatives and risk management.

<p>Conditional probability and conditional expectation provide a way to model uncertainty based on partial information. In finance, they are used to price options, assess risk, and make investment decisions.</p> Signup and view all the answers

<p>Standard Brownian motion is a continuous-time stochastic process that is used to model the random movement of assets. It is fundamental in pricing options, risk management, and simulating financial scenarios.</p> Signup and view all the answers

<p>The moment generating function is a mathematical tool that helps find the moments of a random variable in a convenient way.</p> Signup and view all the answers

<p>The expectation represents the average outcome when an experiment is repeated multiple times.</p> Signup and view all the answers

<p>Discrete distributions assign probabilities to individual values, while continuous distributions assign probabilities to intervals of values.</p> Signup and view all the answers

<p>The moment generating function provides a more convenient method than directly using the probability distribution function.</p> Signup and view all the answers

<p>Expectation is a measure of the average outcome of a random variable, calculated by multiplying each outcome by its probability and summing them up.</p> Signup and view all the answers

<p>These concepts are essential for a basic understanding of probability and provide tools to analyze and predict outcomes.</p> Signup and view all the answers

<p>Sample space (Ω), σ-algebra (Σ), and probability measure.</p> Signup and view all the answers

<p>Discrete random variables have a countable number of possible values, while continuous random variables have a continuous range of values.</p> Signup and view all the answers

<p>A mathematical model specifying the probabilities of possible outcomes for a random variable.</p> Signup and view all the answers

<p>Functions that uniquely determine the probability distribution of a random variable.</p> Signup and view all the answers

<p>Expectations represent the average value of a random variable, capturing its central tendency.</p> Signup and view all the answers

<p>A sample space consists of all possible outcomes of an experiment.</p> Signup and view all the answers